Invariants
| Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $7 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $10^{4}\cdot20^{4}$ | Cusp orbits | $4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20C7 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}1&179\\154&149\end{bmatrix}$, $\begin{bmatrix}49&66\\82&131\end{bmatrix}$, $\begin{bmatrix}59&146\\256&151\end{bmatrix}$, $\begin{bmatrix}169&142\\252&113\end{bmatrix}$, $\begin{bmatrix}269&141\\202&201\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 140.120.7.r.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $192$ |
| Cyclic 280-torsion field degree: | $9216$ |
| Full 280-torsion field degree: | $6193152$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.120.3-20.b.1.3 | $40$ | $2$ | $2$ | $3$ | $0$ |
| 280.24.0-28.f.1.4 | $280$ | $10$ | $10$ | $0$ | $?$ |
| 280.120.3-20.b.1.15 | $280$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.480.13-140.ej.1.5 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-140.el.1.7 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-140.er.1.8 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-140.et.1.7 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-140.fp.1.8 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-140.fr.1.6 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-140.fx.1.3 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-140.fz.1.7 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.bem.1.4 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.bfa.1.2 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.bgq.1.8 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.bhe.1.3 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.bul.1.7 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.buz.1.1 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.bwp.1.2 | $280$ | $2$ | $2$ | $13$ |
| 280.480.13-280.bxd.1.1 | $280$ | $2$ | $2$ | $13$ |